Faraday waves in a square cell network: The effects of varying the cell size

We have conducted experiments of the Faraday instability in a network of square cells filled with water for driving frequencies and amplitudes in the intervals 10 ≤ F ≤ 22 Hz and 0.1 ≤ A ≤ 3 mm, respectively. The experiments were aimed at studying the effects of varying the size of the cells on the surface wave patterns. Images of the surface wave patterns were recorded with a high-speed camera. The time series of photographs composing each video was Fourier analyzed, and information about the waveforms was obtained by using a Pearson correlation analysis. For small square cells of side length l = 2.5 cm, adjacent cells collaborate synchronously to form regular patterns of liquid bumps over the entire grid, while ordered matrices of oscillons are formed at higher frequencies. As the size of the cells is increased to l = 5 cm, collective cell behaviour at lower frequencies is no longer observed. As the frequency is increased, a transition from three triangularly arranged oscillons within each cell to three, or even four, irregularly arranged oscillons is observed. The wave patterns, the waveforms and the energy content necessary to excite Faraday waves are seen to depend on the cell size.